How Concentration Varies With Temperature
With very few exceptions, reaction rates increase with increasing temperature. A rule of thumb used by chemists is that an increase in temperature by 10 oC doubles the reaction rate.
The Collision Theory
The rate constant's dependence on temperature can be explained by collision theory. This theory assumes that, for a reaction to occur, reactant molecules must collide with an energy greater than some minimum value and with the proper orientation. This minimum energy of collision required for two reactant molecules to react is called the activation energy, Ea.
Raising the temperature increases the fraction of molecules having very high kinetic energies. These are the ones most likely to react when they collide. The higher the temperature, the larger the fraction of molecules that can provide the activation energy needed for reaction. The rate constant, k, becomes larger as the temperature increases.The increase in collision frequency with an increase in temperature does not account for the increase in the rate constant. However, f, the fraction of reactant collisions having energy greater than the activation energy, changes rapidly in most cases with even small temperature changes. It can be shown that f is related to the activation energy, Ea, by the equation f = e-Ea/RT.
Transition-State Theory
Collision theory explains some features of a reaction, but it does not explain the role of the activation energy. Transition-state theory explains the reaction resulting from two reactant molecules in terms of an activated complex. An activated complex is an unstable arrangement of atoms that can break up to form products.
When the reactant molecules, A2 and B2 come together with the proper orientation and energy an activated complex is formed in which the old bonds A-A and B-B are being broken and new bonds A-B are being formed. We can also visualize this with a potential-energy diagram such as the one below.
If we assume that the rate constant, k, is directly proportional to
"f", then,
k = cf = ce-E/RT, where c
is a proportionality constant.
Now, if we do a bit on math on this equation we get:
log10 k = log10 c - Ea/2.30 RT
Next, substitute R = 8.31 J/mol.K and let log10 c = A
log10 k = A - Ea / (2.30)(8.31)T
The equation in this form is called the Arrhenius Equation.
You will notice that it is in the form y = a + bx, with y being log10 k and x = 1/T.
A plot of log10 k vs 1/T should be a straight line. Ea for a reaction can be obtained from the slope of this line.
The value of k at a particular temperature can be calculated if it is known for some other temperature. Another form of the Arrhenius Equation is
| log10 (k2 / k1) = (Ea / (2.30)(8.31))(T2 - T1) / T2T1 | This form
is sometimes called the "Two-Point" Equation |